Real Life Applications of GCF and LCM

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Real Life Applications ofGCF and LCM

• How can you tell if a word problem requires you
  to use
• Greatest Common Factor
• or Least Common Multiple
• to solve?

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SWBAT identify and solve real life application
involving GCF and LCM

• Homework GCF/LCM Applications

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GCF and LCMProblem Solving

• First, use our
• PROBLEM SOLVING PROCESS
• What do I know?
• What do I need to know?
• What is my plan?

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GCF Problems may be asking you

• to split things into smaller sections?
• to equally distribute 2 or more sets of items
  into their largest grouping?
• to figure out how many people we can invite?
• to arrange something into rows or groups?

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GCF Example

• Samantha has two pieces of cloth. One piece is 72
  inches wide and the other piece is 90 inches
  wide. She wants to cut both pieces into strips of
  equal width that are as wide as possible. How
  wide should she cut the strips?

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Samantha has two pieces of cloth. One piece is 72
inches wide and the other piece is 90 inches
wide. She wants to cut both pieces into strips of
equal width that are as wide as possible. How
wide should she cut the strips?

• What do I know?
• The pieces of cloth are 72 and 90 inches wide.
• What do I need to find out?
• How wide should she cut the strips so that they
  are the largest possible equal widths.

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Samantha has two pieces of cloth. One piece is 72
inches wide and the other piece is 90 inches
wide. She wants to cut both pieces into strips of
equal width that are as wide as possible. How
wide should she cut the strips?

• What is my plan?
• This problem can be solved using Greatest Common
  Factor because we are cutting or dividing the
  strips of cloth into smaller pieces (Factor) of
  72 and 90 (Common) and we are looking for the
  widest possible strips (Greatest).
• I will find the GCF of 72 and 90

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GCF Word Problem Solution

• GCF using List Method
• 8 x 9 9 x 10
• 6 x 12 6 x 15
• 4 x 18 5 x 18
• 3 x 24 3 x 30
• 2 x 36 2 x 45
• 1 x 72 1 x 90
• GCF using Common Prime Factors Method
• 72 2 x 2 x 2 x 3 x 3
• 90 2 x 3 x 3 x 5
• GCF 2 x 3 x 3 18
• Samantha should cut each piece to be 18 inches
  wide

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LCM Problems may be asking you

• about an event that is or will be repeating over
  and over.
• to purchase or get multiple items in order to
  have enough.
• to figure out when something will happen again at
  the same time.

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LCM Example

• Ben exercises every 12 days and Isabel every 8
  days. Ben and Isabel both exercised today. How
  many days will it be until they exercise together
  again?

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Ben exercises every 12 days and Isabel every 8
days. Ben and Isabel both exercised today. How
many days will it be until they exercise together
again?

• What do I know?
• Ben exercises every 12 days and Isabel every 8
  days and they both exercised today.
• What do I need to know?
• How many days is it until they will both exercise
  on the same day again.

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Ben exercises every 12 days and Isabel every 8
days. Ben and Isabel both exercised today. How
many days will it be until they exercise together
again?

• What is my plan?
• This problem can be solved using Least Common
  Multiple because we are trying to figure out when
  the soonest (Least) time will be that as the
  event of exercising continues (Multiple), it will
  occur at the same time (Common).
• I will find the LCM of 8 and 12.

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LCM Word Problem Solution

• LCM using List Method
• 8 8, 16, 24, 32, 40
• 12 12, 24,
• LCM using Prime Factorization Method
• 8 2 x 2 x 2
• 12 2 x 2 x 3
• (only use the common factors once)
• LCM 2 x 2 x 2 x 3 24
• They will exercise together again in 24 days.

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Bachelors Practice

• Tell whether each problem is LCM or GCF then
  solve
• Nicole found gift bags in packs of 13 and bows in
  packs of 2. If Nicole wanted to have the same
  number of gift bags as bows, what is the smallest
  number of gift bags she would have to buy?

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QUIZ!!!!!!

• On a sheet of notebook paper, tell whether the
  following word problems could be solved using GCF
  or LCM

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Question 1

• Mrs. Evans has 120 crayons and 30 pieces of paper
  to give to her students. What is the largest of
  students she can have in her class so that each
  student gets equal of crayons and equal of
  paper.

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Question 2

• Rosa is making a game board that is 16 inches by
  24 inches. She wants to use square tiles. What
  is the larges tile she can use?

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Question 3

• Z100 gave away a Z 100 bill for every 100th
  caller. Every 30th caller received free concert
  tickets. How many callers must get through before
  one of them receives both a coupon and a concert
  ticket?

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Question 4

• Two bikers are riding a circular path. The first
  rider completes a round in 12 minutes. The second
  rider completes a round in 18 minutes. If they
  both started at the same place and time and go in
  the same direction, after how many minutes will
  they meet again at the starting point?

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Question 5

• Sean has 8-inch pieces of toy train track and
  Ruth has 18-inch pieces of train track. How many
  of each piece would each child need to build
  tracks that are equal in length?

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Question 6

• I am planting 50 apple trees and 30 peach trees
  in rows. I want to mix the apple and peach trees
  in my rows, and I want each row to be the same.
  What is the maximum number of trees I can plant
  per row?

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QUIZ Answers

• 1.) GCF
• 2.) GCF
• 3.) LCM
• 4.) LCM
• 5.) LCM
• 6.) GCF

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QUIZ!!!!!!

• Nowfor some further practice, try to solve each
  of the 6 real-life application problems. Be
  sure to give a sentence form answer that
  incorporates your LCM or GCF solution.
• Here are the real-life situations once again

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Question 1

• Mrs. Evans has 120 crayons and 30 pieces of paper
  to give to her students. What is the largest of
  students she can have in her class so that each
  student gets equal of crayons and equal of
  paper.

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Question 1 ANSWER

• Mrs. Evans has 120 crayons and 30 pieces of paper
  to give to her students. What is the largest of
  students she can have in her class so that each
  student gets equal of crayons and equal of
  paper.
• Answer GCF 30
• Mrs. Evans could have 30 children in her class,
  each of whom will receive 1 piece of paper and 4
  crayons.

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Question 2

• Rosa is making a game board that is 16 inches by
  24 inches. She wants to use square tiles. What
  is the larges tile she can use?

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Question 2 ANSWER

• Rosa is making a game board that is 16 inches by
  24 inches. She wants to use square tiles. What
  is the larges tile she can use?
• GCF 8
• The largest tile Rosa can use is 8 inches by 8
  inches. She will have a total of six 8 square
  tiles on her game board.

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Question 3

• Z100 gave away a Z 100 bill for every 100th
  caller. Every 30th caller received free concert
  tickets. How many callers must get through before
  one of them receives both a coupon and a concert
  ticket?

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Question 3 ANSWER

• Z100 gave away a Z 100 bill for every 100th
  caller. Every 30th caller received free concert
  tickets. How many callers must get through before
  one of them receives both a coupon and a concert
  ticket?
• Answer LCM 300
• The 300th caller will be the first to receive
  both a Z 100 bill and a concert ticket.

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Question 4

• Two bikers are riding a circular path. The first
  rider completes a round in 12 minutes. The second
  rider completes a round in 18 minutes. If they
  both started at the same place and time and go in
  the same direction, after how many minutes will
  they meet again at the starting point?

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Question 4 ANSWER

• Two bikers are riding a circular path. The first
  rider completes a round in 12 minutes. The second
  rider completes a round in 18 minutes. If they
  both started at the same place and time and go in
  the same direction, after how many minutes will
  they meet again at the starting point?
• ANSWER LCM 36
• The two bikers will meet at the starting point
  again in 36 minutes.

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Question 5

• Sean has 8-inch pieces of toy train track and
  Ruth has 18-inch pieces of train track. How many
  of each piece would each child need to build
  tracks that are equal in length?

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Question 5 ANSWER

• Sean has 8-inch pieces of toy train track and
  Ruth has 18-inch pieces of train track. How many
  of each piece would each child need to build
  tracks that are equal in length?
• ANSWER LCM 72
• Sean will need 9 of his 8 track pieces and Ruth
  will need 4 of her 18 track pieces in order to
  build tracks of equal length. The length of the
  tracks will be 72.

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Question 6

• I am planting 50 apple trees and 30 peach trees
  in rows. I want to mix the apple and peach trees
  in my rows, and I want each row to be the same.
  What is the maximum number of trees I can plant
  per row?

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Question 6 ANSWER

• I am planting 50 apple trees and 30 peach trees
  in rows. I want to mix the apple and peach trees
  in my rows, and I want each row to be the same.
  What is the maximum number of trees I can plant
  per row?
• ANSWER GCF 10
• I will have 10 rows and each row will have 5
  apple trees and 3 peach trees.

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GREAT JOB!

• You are learning to be quite the
• Problem Solver!